Problem: Solve for $q$, $ -\dfrac{5}{15q - 5} = \dfrac{9}{3q - 1} - \dfrac{4q + 5}{3q - 1} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15q - 5$ $3q - 1$ and $3q - 1$ The common denominator is $15q - 5$ The denominator of the first term is already $15q - 5$ , so we don't need to change it. To get $15q - 5$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{9}{3q - 1} \times \dfrac{5}{5} = \dfrac{45}{15q - 5} $ To get $15q - 5$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{4q + 5}{3q - 1} \times \dfrac{5}{5} = -\dfrac{20q + 25}{15q - 5} $ This give us: $ -\dfrac{5}{15q - 5} = \dfrac{45}{15q - 5} - \dfrac{20q + 25}{15q - 5} $ If we multiply both sides of the equation by $15q - 5$ , we get: $ -5 = 45 - 20q - 25$ $ -5 = -20q + 20$ $ -25 = -20q $ $ q = \dfrac{5}{4}$